In NMR (nuclear magnetic resonance), a superconducting magnet is utilized to produce a magnetic field. The uniformity of the magnetic field is only between about 1.0.times.10.sup.-5 to 1.0.times.10.sup.-6 at best. However, in recent years, magnetic fields of quite high uniformities of 1.3.times.10.sup.-9 to 1.0.times.10.sup.-10 have been required. Accordingly, it is common practice to provide a corrective magnetic field-generating apparatus for compensating for magnetic field nonuniformities.
Some technical terms used herein are defined below. First, elements for producing a corrective magnetic field are referred to as shims. A set of coils energized with an electrical current to provide a magnetic field correction is referred to as an electrical current shim. A shim which is disposed near the center of a magnet for producing a principal magnetic field and which operates at room temperature is referred to as a room-temperature shim. The present invention especially relates to a room-temperature shim and so a room-temperature shim may be simply referred to as a shim hereinafter.
Referring to FIG. 6, a corrective magnetic field-generating apparatus is normally composed of a shim 1, a power supply 2 for supplying an electrical current to the shim, and a control unit 3 for controlling the power supply according to information given from the outside. This corrective magnetic field-generating apparatus produces a corrective magnetic field to cancel out nonuniform components of the principal magnetic field or to vary the uniform magnetic field. The principal magnetic field is set up by a magnet 10 which is a superconducting magnet having superconducting solenoid coils in NMR.
The present invention is directed to a region around the center of the magnet 10 producing the principal magnetic field. In FIG. 6, the center of the magnet 10 is taken at the origin. The center axis is taken on the z-axis. The x- and y-axes to lie on a plane orthogonal to the z-axis. Let r, .THETA. (theta), and .phi. (phi) be three components of a polar coordinate system. It is known that the z-axis component B.sub.z of the magnetic field near the origin in the magnet 10 is given by ##EQU1##
Generally, in the center of a magnet of high uniformity, the x-axis and y-axis components of the magnetic field are sufficiently smaller than the z-axis component and thus can be neglected. Therefore, only the z-axis component B.sub.z of the magnetic field is considered in the following discussion.
In Eq. (1) above, A.sub.0 indicates the magnitude of a uniform magnetic field component. The other components indicate the magnitudes of nonuniform magnetic field components. Indicated by n and m are integers not less than 0. A.sub.n.sup.m and B.sub.n.sup.m are constants. P.sub.n.sup.m (cos .THETA.) is an associated Legendre function. Where m=0, m will be omitted hereinafter. For example, A.sub.1.sup.0 is simply referred to as A.sub.1, and P.sub.n.sup.0 (cos .THETA.) is simply referred to as P.sub.n (cos .THETA.).
A magnetic field assuming a value independent of .phi. shown in FIG. 6 within a plane perpendicular to the z-axis is herein referred to as an axial magnetic field. A magnetic field taking a value dependent on .phi. is referred to as a rotation direction magnetic field. In Eq. (1), the first and second terms with m=0 and not dependent on .phi. indicate axial magnetic field components. The third term with m.noteq.0 and dependent on .phi. indicates rotation direction magnetic field components.
The x-axis and y-axes are rotated around the z-axis through angles of (2.pi./M).times.k (M=2, 3, 4, . . . ; for each value of M, k=1, . . . , M-1). As a result, those magnetic fields which appear exactly the same as the magnetic field not rotated at all, i.e., k=0, exist. These magnetic fields are referred to as M-times-rotation-symmetric magnetic fields or simply as rotation-symmetric magnetic fields.
Magnetic field components corresponding to the constants A.sub.n.sup.m and B.sub.n.sup.m of the z-axis magnetic field components which can be expressed by Eq. (1) are referred to as the A.sub.n.sup.m and B.sub.n.sup.m components of the magnetic field or simply as A.sub.n.sup.m and B.sub.n.sup.m. Where A, B, and m are different the magnetic field components are different in dependence on angle. Therefore, the constants A.sub.n.sup.m and B.sub.n.sup.m are magnetic field components which are different in dependence on angle. A.sub.n.sup.m and A.sub.k.sup.m (n.noteq.k) are magnetic field components which have the same dependence on angle.
Those components of the z-axis magnetic field component produced by a shim which are intentionally controlled are referred to as controlled magnetic field components. Of these controlled magnetic field components, magnetic field components used to vary uniform field components and to compensate for nonuniform field components are referred to as corrective magnetic field components.
Accordingly, "corrections of magnetic field" encompass variations of uniform field components, as well as corrections of nonuniform field components.
A conventional configuration of the corrective field-generating apparatus shown in FIG. 6 is described in U.S. Pat. No. 3,287,630. This apparatus comprises four groups of coils (Z' coils, Z.sub.1 " coils, Z.sub.2 " coils and Z"' coils) for correcting axial magnetic field components and four groups of coils (X coils, Y coils, X-Z coils, and Y-Z coils) for correcting rotation direction field components.
Each group of coils consists of one or more pairs of coils connected in series. Each group produces one corrective magnetic field component. A shim consisting of such series combination or combinations of coils is referred to as a series shim herein.
The corrective magnetic field component produced by the series shim is determined by the positions of the coils, their shape, the directions of electrical currents, and the number of turns. As a consequence, the structure of the shim is complicated. Also, the coils have to be designed with a very limited number of degrees of freedom. It is difficult to reduce the heat produced by the coils by reducing the energizing current. In this way, various problems exist.